Sunday, 6 December 2009



An article "Time Warp: how your brain creates the fourth dimension" in the 24 October 2009 issue of the New Scientist was particularly stimulating. Taking the 'Wagon Wheel effect' of cinematography which is due to the mismatch between the speed of rotation of the wheel and the frame rate, the author argues that similar effects can be observed due to the operation of the human brain. The human eye collects data as samples and that there is a natural sampling rate within the brain. If data is presented at the edges of the sampling intervals then it is not seen and that this is a large part of the art of the conjurer.

I have observed another form of wagon wheel effect while stopped at a traffic light at a T-junction that includes a pedestrian crossing. In UK these are fenced off. The galvanised rails comprise 10mm square cross-section rods, set 100mm apart as seen in the picture. Now, if from your parked position you watch the progress of a car wheel through the railings, then, depending on the speed of the car you will see the perforations on the wheel rim rotate at a different speed to the wheel itself. Does anyone know if this effect has a specific name?
Did anyone see the article in the Daily Telegraph which is on their website
http://www.telegraph.co.uk/science/6439621/How-maths-makes-the-world-go-round.html ?

It really annoyed me because of a myth that seems to be perpetuated. The article was praising a new book by Ian Stewart who for many years contributed to Scientific American when Martin Gardner gave up his wonderful "Mathematical Games" slot. I have not read the book yet, but a title " How maths makes the world go round" is indeed very worrying. The sub-title " Whether you’re searching for oil, the lost chord or a better kind of carrot, mathematics is the key, says Ian Stewart" is irrefutable, but the article in the Telegraph gave the impression that first God created mathematics and then the of his world conformed to this formalism. People already have problems with mathematics and its teaching which such a thesis would do nothing to dispel. When I taught mathematics I reminded students of the apocryphal story that the dictionary of Inuit has hundreds of words to describe the quality of snow, but only a few to describe the quality of vegetation. This was because that language needed to express concepts to the Inuit people which are important for them, but are not necessarily important to someone living in the UK. We talk about being able to express thoughts in one language which cannot be easily expressed in another. Gemütlich is a single word which expresses something in German that requires multiple words in English. So, armed with these thoughts I explained to students that mathematics is merely a language which has its own vocabulary, grammar and syntax. It is a very useful language because the shorthand 'sine' and 'cosine' are used to save someone doing a lot of out-of-phase hand-waving. When students absorbed this concept, then the learning of mathematics suddenly lost its mystique. So, to Professor Stewart and the Daily Telegraph I would have to say that the wonderful world in which we live is amenable to the mathematics that we have developed, just as it is amenable to description in any other language. Where we observe something that is outside current formalism, then we have to develop new mathematics. The journalist who wrote the Daily Telegraph article talks about Fourier analysis. Today most students on mathematical science courses will learn about this at an early stage and yet, in 1857, when people were uncertain about the feasibility of laying an Atlantic telegraph cable, there was mention that Professor Thomson (later Lord Kelvin) of Glasgow University "was one of the few people in Britain who understood the new techniques of Monsieur Fourier". If we come closer to our own time and look at the efforts which Oliver Heaviside had to go through to derive some of his ground-breaking results we can be awe-struck by the tenacity of the man. Today, armed with a mathematical curiosity which is entirely imaginary (the square-root of minus one), science and engineering students can easily deliver the same results. The world is wonderful. Mathematics is wonderful, but let us please not perpetuate a myth which makes the situation even more opaque for so many.
This is a story which is recorded in two parts. The encounter upon which these are based occurred in early September 2006 and shortly afterwards when I was already in Shanghai a news disclosure prompted me to make a record of the first part of this story which I will refer to as a collusion hypothesis.
*****
The recent (mid 2006) publicity about collusion between the armed forces and loyalists in Northern Ireland should really not have come as a surprise to anyone who tried to analyse events beyond the immediate. I would like to add some information about a meeting that I had that, at least for me, seemed to cast so much light on so much of the happenings in NI since 1968. People seem to have forgotten that British troops were sent there to protect the minority in the unpleasant aftermath of the civil rights marches. People have long forgotten that James Callaghan was feted as a hero in the Bogside. Slowly and inexorably the emphasis changed. The protected became the villains. This process was accelerated when the Wilson government was replaced by the Heath administration. Internment and Bloody Sunday followed and these were points of no return. So, how/why did this come about? I think that I might now have some pointers and would like to draw a hypothesis which was given strength by an amazing conversation that I had in early September 2006 when I met a man who had been a senior officer in Northern Ireland, someone who was able to boast that during his period of command he had not lost a single man. Whereas presence in conflict zones damages many people, it had not done this for him. If anything the experience had enhanced him. He relished the challenge and was fascinated by the paradoxes that he encountered. He liked a bit of stone-throwing when they were on patrol "You knew that everything was okay. If there was no jeering/stone throwing then you knew that something was up and you called for back-up". "Over my time there I gained the begrudging respect of the catholic population, which was all that I wanted. It was July, the 'Marching Season' that was just so crazy, so screwy. Here you were, having had the Catholics throw stones at you all year, standing between them and the loyalists. The Catholics were handing you cups of tea, while the loyalists were lobbing bricks at you. One time I was in an armoured car at the front-line, writing a report when a brick somehow got through the window and hit my wrist - it didn't half hurt. I was out of there like a shot and ordered the snatch squad out to get the little bastard that had hit me. What they dragged over was such a wimpish little specimen and when I asked him why he had done that I got a tirade of abuse about denying them their right to march. I had him banged up for six months".

Finding a person who was quite clearly of an open mind I posed him the question that had worried me for such a long time. Why was it that a force that had been sent to protect the Catholics had been so transformed in purpose? He agreed with every point raised. He said that it was entirely brain-washing that all had undergone during the pre-tour-of-duty training. They had been prepared to deal with a belligerent population that was hell-bent on their destruction. What he and fellow officers encountered was completely at variance to their expectations. He and they found that they had to go against their training and adjust their strategy on-the-fly as circumstances on the ground permitted. "I did it by adopting a system of frequent, in-depth patrols". I made it clear that if the population did not cause me any problems, then I would reciprocate, and it worked".

He said that he found my questions raised questions that had been in his own mind. I put to him the hypothesis that there were forces (individual and/or groups) within the UK military that had agendas that were not necessarily in harmony with official Government policy. I believed that these parties were unhappy with the alteration of the status-quo that followed the events in Northern Ireland from October 1968 onwards. Although the army had been sent to protect the nationalist population, it was possible to influence the mindset of individual servicemen through a very effective propaganda apparatus. I had seen the husband of a friend of a friend who had been posted to NI in 1969 was in a very short time intensely antagonistic to the catholic minority. Later, when I was Deputy Warden in Rutland Hall, in Nottingham I found that one of my resident tutors was very biased in his attitudes to the Irish problem. His father was in the army and was then based in NI.

So, who are these forces? How did they acquire their power and do they still wield this power?

Some sort of answer seems to have come from a programme on BBC TV called "The Plot Against Harold Wilson". It was clear in the programme that there were forces in the military who disagreed with much of the Wilson policies. I certainly remember an exercise where there was a sudden strong military presence at Heathrow Airport. What I had not realised was that it was undertaken without the knowledge of the Government. It was believed to have been intended as a warning to the Government that the army could mount a coup d'etat, if it found it necessary to do. But, why would any army, the servants and defenders of the State want to do that? The programme pointed the finger of blame at Earl Mountbatten and his supporters and there has not been much to refute that.

Now, if an army can collude against its own government, then should we be surprised that it colluded with loyalists in order to preserve what it wished to be the status-quo in Northern Ireland? The question should not be whether this happened or not, but whether it happened with the knowledge and approval of the Government? Depending on the response to that question, there should be another question, namely, what steps are HM Government taking to limit any ex-jure activities of its military forces?

There is another question that does not appear to have been asked and that is the extent of contact and possible collusion between some within the army in Northern Ireland and Republican sympathisers? This was perhaps less unusual than one might think. My informant had reason to visit certain Ulster prisons and developed a profound respect for republican prisoners, for their discipline and for their use of time in prison to pursue personal study. On the other hand, he found Loyalist cells full of hate messages, body-building kit and heavily tatooed occupants. So, if this individual view was shared by others who might be less scrupulous, then one could conceive that the boundaries between respect and collusion could in places be blurred. I therefore ask again if there was substantial army/republican fraternisation, sanctioned or otherwise?

I have an as yet unsubstantiated hypothesis that the eventual assassination of Earl Mountbatten could have been the result of collusion between certain republicans and members of UK security forces. For many years Mountbatten and his family had been holidaying in the same place in the Irish Republic and, although there could have been many opportunities to kill him, these had not been taken. So, why then? From his side, his disdain of the dangers to personal security might be viewed as a form of arrogance as he would never have accepted that a part of Ireland had seceded from the Empire. However, many years ago someone told me that he had a particular liking for activities not dissimilar to those mentioned in "One Girls War". Although it was well known in certain circles, it was never discussed (just as John Major's affair was known but not discussed). Nevertheless, there was an indication that in 1979 it was threatening to become a major source of embarrassment to the Royal family. If any of this is true then how convenient it would be if the man who appears to have been the architect of UK military policy re-alignment in Northern Ireland should perish a hero.
*****

The second story relates to the same informant and committing this to record at this point was occasioned by the 20th anniversary of the fall of the Berlin Wall. He was in Berlin in November 1989 and relates how strange it was that at a critical time, when events were unfolding so quickly in Eastern Europe all senior commanders of the Four Powers were in conclave somewhere in Bavaria and thereby incommunicado when things started to happen in Berlin.

People in West Berlin had only an inkling of what was happening and his report of how the lower echelons of command of the Western Powers reacted is particularly illuminating. The French pointed out that whatever was happening on the other side of the Wall, it was not in their Sector and therefore not their problem. The Americans were convinced that an attack was imminent and brought out every tank onto the streets facing the Wall in their Sector. The British, meanwhile, loaded up their trucks and drove up to the Wall, left their armaments in the trucks and set up trestle tables against the Wall. As holes started to appear, they passed through cups of tea.

He then went on to relate how, with the collapse of the Soviet Union their lines of supply disappeared. There was a Soviet barracks in Potsdam where the troops only survived as a result of food supplied by the British. In return for this kindness their benefactors were allowed access to (allowed to play with) the tanks and other equipment which until a short time before had been threatening them - it was great fun.